This document presents a proposed algorithm for removing Gaussian noise from images using shift invariant wavelet transform. It begins with an introduction that outlines the objectives of noise removal and discusses image noise and types of noise. It then covers wavelet transforms, discrete wavelet transform, wavelet-based image denoising techniques including thresholding. The proposed algorithm applies shift invariant denoising using soft or hard thresholding. Experimental results on various test images like Cameraman, Baboon and Lena show that the shift invariant wavelet denoising provides better PSNR and MSE values compared to traditional wavelet denoising.

1. Removal of Gaussian Noise Using Shift
Invariant Wavelet Transform
July 31, 2013
Department of
Information
Technology
Presented by
Priyanka Sharma
Guided By
Dr. Manish Shrivastava

2. Outlines
• Introduction
• Objective
• What is noise?
• Image noise
• Types of noise
• Noise source
• Denoising Artifacts
• Image denoising
• Classification of image denoising algorithm

3. Contd.
• Wavelet transform
• Discrete wavelet transform
• Wavelet based image denoising
• Wavelet Thresholding
• Disadvantage of DWT
• Shift invariant denoising
• Proposed algorithm based on TI denoising
• Experimental Result and analysis
• Conclusion
• Future Work
• References

4. Introduction
• What is Image?
• Still Image :- stationary or motionless image
• Problem with Still Image:-
1.Pixels are highly correlated
2.Subjective Redundancy
• Solutions
1.HVS
2.DWT
3.SHIFT INVARIANT
• Aim of research

5. Objective
The main objective are
• Proposing a denoising algorithm with coding
scheme less complex and applicable in real time
situation.
• Proposing an denoising algorithm which gives
more PSNR and less MSE and better visual
perception.
• Analytical and experimental validation of
proposed algorithm of denoising using MATLAB.

6. What is noise?
• Wiki definition :- Noise is unwanted signal
• One person’s signal is another one’s Noise
• Noise is not always Random.
• Noise is not always bad ex. Stochastic
resonance

7. Image Noise
• Wiki Definition:- It is a random variation in
brightness and color of image
• Where does noise come from?
Sensor(Thermal and electrical interference)
Environmental condition (Rain, Snow etc.)
• Example:- Blurring
Dots on image

8. Types of Noise
• Gaussian noise
• Speckle noise
• Salt and Pepper noise
• Shot noise
• Quantization noise
• Brownian noise

9. Noise sources

10. Image Denoising
• Removal of unwanted noise in order to restore
original image.
• Why do we want denoising?
 Visual unpleasant
 Bad for Compression
 Bad for Analysis

11. Denoising Artifacts
• Blur
• Ringing/ Gibbs phenomena
• Staircase effect
• Checkerboard effect
• Wavelet outliers

12. Classification of image denoising
algorithm
• Spatial domain filtering-
linear filter
nonlinear filter
• Transform domain filtering-
Fourier transform
Wavelet transform
Miscellaneous transform such as Ridglets,Curvelet

13. Wavelet transform
• A wavelet is a “small wave” that has its energy concentrated in time
and frequency. It provides a tool for the analysis of transient, non-
stationary, and time-varying phenomena.
• Wavelet transform is capable of providing the time and frequency
information simultaneously, hence giving a time-frequency
representation of the signal.
• There are mainly two types of Wavelet Transforms-
Continuous Wavelet Transformation (CWT)
Discrete Wavelet Transformation (DWT)

14. Discrete wavelet transform
• Why it is Better then CWT ?
 Non- redundant
 Sufficient information for analysis and synthesis
 Reduction in computation time
• Why it needed here ?
 Better spatial resolution and spectral localization
 Operation based on amplitude rather than
spectra

15. Wavelet based image denoising
• It involve three steps
1. Forward wavelet transform

16. CONTD.
2. Estimation:- Thresholding, Shrinking.
3. Inverse wavelet transform

17. Wavelet Thresholding
There are two type of thrsholding
• HARD THRESHOLDING
D (U, λ) = U for all |U|> λ
= 0 otherwise

18. Contd.
• SOFT THRESHOLDING
• D (U, λ) = U- λ If |U|≥ λ
= 0 If |U|<λ

19. Disadvantage of DWT
• Shift sensitivity
• poor directional selectivity
• Gibbs phenomenon

20. Shift Invariant denoising
• Why it is used?
To suppress Artifacts
• How it work?
Shifts in Time and Frequency
Averaging Shifts

21. Contd.
• Block diagram presentation
Noisy image
shift(mK,nK) WD shift(-mK,-nK)
shift(m1,n1) WD shift(-m1,-n1)
Avg
denoised
image



22. Proposed algorithm Based on TI
Denoising
• Resize Image to 256x256 pixels Size.
• Add Gaussian Noise of given mean and variance to Image.
• Estimate the Threshold using ‘sureshrink' (threshold selection using
principle of Stein's Unbiased Risk Estimate).
• Perform N Level Invariant Wavelet Decomposition of Image using
given Wavelet.
• Apply Soft or Hard Thresholding on Decomposed Wavelet
Coefficients.
• Perform N Level Inverse Shift Invariant Wavelet Transform using
given Wavelet.
• Calculate the PSNR and MSE.

23. Flow Chart

24. Experimental result and Analysis

25. Contd.

26. Contd.

27. Contd.

28. Contd.

29. Contd.

30. Contd.

31. Contd.

32. Contd.

33. Contd.

34. Contd.

35. Contd.

36. Contd.

37. Contd.

38. Contd.

39. Contd.

40. Result Analysis Table
Performance of Cameraman image in terms of PSNR and MSE
Wavelet
Analyzer
Soft Thresholding Hard Thresholding
Wavelet
Denoising
Shift
Invariant
Wavelet
Denoising
Shift
Invariant
PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE
Haar
23.0027 325.6916 25.0989 200.9663 23.32 302.4996 25.4805 184.0884
Daubichies 23.0027 325.6916 25.0989 200.9663 23.32 302.4996 25.4805 184.0884
Symmlet
23.5435 287.562 24.9449 208.2539 23.727 275.6642 25.1966 196.5253
Coiflet
23.4875 291.2929 24.9439 208.3002 23.64 281.244 25.1779 197.3752

41. Result Analysis Table
Performance of Baboon image in terms of PSNR and MSE.
Wavelet
Analyzer
Soft Thresholding Hard Thresholding
Wavelet
Denoising
Shift
Invariant
Wavelet
Denoising
Shift
Invariant
PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE
Haar
23.0953 318.8246 25.0258 204.4097 23.449 293.8837 25.1996 196.3889
Daubichies 23.0953 318.8246 25.0258 204.4097 23.449 293.8837 25.1996 196.3889
Symmlet
23.654 283.4942 24.8041 215.1124 23.6261 282.1451 24.895 210.6598
Coiflet
23.4454 294.1341 24.7844 216.0936 23.5466 287.3574 24.8654 212.0983

42. Result Analysis Table
Performance of Leena mage in terms of PSNR and MSE
Wavelet
Analyzer
Soft Thresholding Hard Thresholding
Wavelet
Denoising
Shift
Invariant
Wavelet
Denoising
Shift
Invariant
PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE PSNR(dB) MSE
Haar
23.7587 273.6699 25.9334 193.9986 23.8079 302.4996 26.0002 184.0884
Daubichies 23.7587 273.6699 25.9334 193.9986 23.8079 302.4996 26.0002 184.0884
Symmlet
24.2669 243.4387 25.7304 203.6884 24.2682 275.6642 25.749 196.5253
Coiflet
24.3151 240.7499 24.702 204.4207 24.3308 281.244 25.7154 197.3752

43. Graphical analysis PSNR and MSE value for cameraman image

44. Graphical analysis PSNR and MSE value for leena image

45. Graphical analysis PSNR and MSE value for image of baboon.

46. Conclusion
• From the simulation analysis, the wavelet
transform in image denoising in particular
stationary images, can effectively remove noise
and improve SNR. With regard to complexity of
image structure, invariant wavelet transform
denoising can play the advantages compared to
traditional denoising, invariant wavelet can better
demonstrate its advantages. From the simulation
results, we also obtain that use the principle of
sureshrink threshold can effectively reduce noise,
and can retain a useful component of image.

47. Future Work
• This algorithm can be implemented for
removal of salt and pepper noise, Impulsive
noise.
• Denoising of color image can also possible by
slightly modification on this algorithm.

48. References
• R. C. Gonzalez and R .E Wood. Digital image processing
Prentice Hall, Upper saddle river, N.J 2nd edition 2002.
• S.Kother Mohideen, Dr. S. Arumuga Perumal, Dr.
M.Mohamed Sathik, “Image De-noising using Discrete
Wavelet transform”, IJCSNS International Journal of
Computer Science and Network Security, VOL.8 No.1,
January 2008
• Sachin D Ruikar, Dharmpal D Doye “Wavelet Based
Image Denoising Technique” (IJACSA) International
Journal of Advanced Computer Science and
Applications,Vol. 2, No.3, March 2011

49. Contd.
• Shuren Qin, Changqi Yang, Tang Baoping and
Shanwen Tan “THE DENOISE BASED ON
TRANSLATION INVARIANCE WAVELET
TRANSFORM AND ITS APPLICATIONS”
• R.R. Coifman and D.L. Donoho Translation-
Invariant De-Noising, Yale University and Stanford
University.
• Harnani Hassan, Azilah Saparon “Still Image
Denoising Based on Discrete Wavelet Transform”
2011 IEEE International Conference on System
Engineering and Technology (ICSET).

50. Contd.
• Mukesh C. Motwani ,Mukesh C. Gadiya ,Rakhi C.
Motwani “Survey of Image Denoising
Techniques”.
• D.L. Donoho, ‘Denoising by Soft Thresholding’,
IEEE Translations on Information Theory, vol. 14,
pp.613-627, 1995.
• Lakhwinder Kaur, Savita Gupta, R.C Chaulan,
‘Image Denoising using Wavelet Thresholding’,
Indian Conference on Computer Vision , Graphic
and Image Procesing, Ahmedabad, Dec. 2002

51. Contd.
• Jaideva C. Goswani, Andrew K. Chan,
‘Fundamentals of Wavelet:Theory, Algorithm,
and Applications’, John Wiley & Son Inc.,1999.
• Bui and G. Y. Chen, ‘Translation invariant
denoising using multiwavelets’, IEEE on Signal
Processing, Vol 46, no 12, pp.3414-3420, 1998

52. `
THANK YOU